Apparatus for measuring dynamic characteristics of systems by crosscorrelation



United States Patent 3,354,297 APPARATUS FOR MEASURING DYNAMIC CHA ACTERISTICS OF SYSTEM BY CR O RELAT QN George W. Anderson, Santa Ana, and John A. Aseltine, S ng al f-L an Geo e onner Lafay tte, Int l., assignors to Ford Motor Company, Deafborn, Mich., a corporation of Delaware Continuation of application Ser. No. 1,935, Jan. 12, 1960. This application Feb. 6, 1964, Ser. No. 343,917 5 Claims. (Cl. 235-.-181) ABSTRACT OF THE DISCLOSURE Apparatus for measuring dynamic characteristics of systems by crosscorrelation using a periodic, discreteinterval binary test signal having'a nonasymptotic autocorrelation function of triangular form.

This application is a continuation of our now abandoned copending application Serial No. 1,935, filed Jan. 12, 1960, and entitled Crosscorrelator.

i invention ela s to appara us or easurin dynamic characteristics of systems. Typical examples of measurable systems according to the invention are machine tools with programmed automatic controls, chemical manufacturing processes, and oil refinery control systems. It is conventional to determine the dynamic characteristics of such systems by exciting the system with a sinusoidal or step function input and measuring the output response. However, this technique requires the systerm to be out of normal operation and it'is often desirable to measure the dynamic characteristics of a system while in operation. This type of measurement provides a continuous check on the sy'stems characteristics and does not require any loss of production time. It is essential that such measurements be made Without disturbing the operation of the system and a general approach to this end using a crosscorrelation technique has been developed. A general description of crosscorrelation techniques may be found in a paper entitled A Self-Adjusting System for Optimum Dynamic Performance, presented at the IRE national convention, March 25, 1958, and in the references cited therein.

In general a crosscorrelator should be able to compute the crosscorrelation function of an operating physical system Without materially disturbing the system. Furthermore, the crosscorrelation computations should be immune to the effects of noise in the system, command signals, and parameter changes. The crosscorrelation function of a system can be determined from the impulse response of the system and the autocorrelation function of the input signal. When the input signal has a bandwith considerably larger than that of the system under test, i.e., on the order of three to ten times larger, then its autocorrelation function will b; @fiestively an impulse and the impulse response of the system Will be equal to the crosscorrelation function. A determination of the crosscorrelation coefiicient at a number of points in time will provide the impulse response of the system,

In its crudest form, a crosscorrelator may measure the input to the system and the output of the system and from these calculate the crosscorrelation function. Practically, this approach is very difiicult since there is no cont e t e nnt Si Crosscorrelators have been developed in which the input or test signal is generated in the crosscorrelator and s i je e to th system as n ut in se i n tin w other inputs to the system. The crosscorrelation between the test signal input and the systems output giyes the desired impulse response measurement. The test signal source in such instruments usually generates a random noise connotes m n t de and sh i i nt bandw d h to avoid disturbing the system under test. Such instruents" t i a nu e f s sadv n h e innh hing e qu e en of a a d n n s ene at r and t e ren i hn n of a ge, long i e cons an fi te s o pr v d the ne es y a? a A r in y n bi c o the P e nve t on t pmvitie a new n mp ved s n rela or whic i simpler inde'si gn and operatioii and which providesbetter performarice than previously known instruments. Another je i 'tn p i a c s nr cl t r wh h ines 9 require a random noise input signal. A further object is to provide a crosscorrelator which uses an input test signal that is p n d s: and bina y' n t n rat er a bein random noise.

Summary According to the invention apparatus is provided which utilizes a periodic, discrete-interval binary test signal to provide an autofco'rrelation function which has a triangular form, a controllable width, and which is nonasymptotic. The crosscorrelaipr utilizes an input signal which has an autocorrelation function that very nearly approaches the ideal impulse function. i

The crosscorrelator includes a test signal source, means tor coupling the test signal to the system being measured, means for generating a plurality of successiy'ely delayed versions of the test signal, a plurality of multipliers, each arranged to supply the product of one of the delayed signa ls and the system output, a plurality of low pass filters responsive to the product signals for producing a plurality rif -averaged product signals, and means for recording the averaged product signals} Each multiplier may 'be a bina y d whi h i ac ua ed y 1 9 h de ayed si nals to couple either the "systems output or' theinve'rse of the systems output to an associated filter. The averaged product signals may be recorded for subsequent use, may be displayed for immediate inspection, or may be utilized further circuitry for control purposes and the like.

' The crosscorrelator may use a circulating shift register in the form of a memorydrurnwhich has a timing track in conjunction with a plurality of gates to provide a plurality of relatively long delayed outputs from a periodic s a w c has a re a ve a e n mber a i i nto ni n' n uch ppa a u ten stan of delay n e Pro ided n' inq e nn s o o -h n t e a cond- Drawings a m r d i ed version of the system of FIG. 4,

FIG. 1 discloses a crosscorrelator suitable for use in measuring the dynamic characteristics of a system While the system is in operation. The crosscorrelator includes a signal source 11, a delay unit 12, a multiplier unit 13, a filter unit 14, and a recorder 15. Typically, the system 10 may be an automatic machine tool which has one or more internal feedback loops and an input 18 and output 19. Command signals are coupled to the input 18 and the system may also be subject to parameter disturbances including noise, power source variations, changes in environmental conditions, and the like.

The signal source 11 generates a test signal that is supplied, along with the command inputs, to the system input 18 through a summing unit 20. The test signal is also coupled to the delay unit 12. The delay unit generates a plurality of successively delayed versions of the test signal on lines 21a, 21b, 21in. Each delay signal produces a point on the impulse response curve of the system being tested. The total number of delayed signals and their time spacing are selected to provide a suitable number of appropriately spaced points for the particular system under test. The multiplier unit 13 comprises a plurality of individual multipliers, each of which receives one of the delayed signals and the system output and produces a product signal on a corresponding one of the lines 22a, 2212, 2211. The filter unit 14 includes a plurality of low pass filters which produce a corresponding plurality of averaged product signals on lines 73a, 23b, 2311. The recorder may be any of various conventional recording or indicating devices such as an n-channel pen recorder which produces continuous charts of each input, an oscilloscope with a suitable time base for displaying all of the points on the response curve, or a digital storage device which stores the outputs for further computation and control.

When any system is excited with a random input, its output and input will be correlated to an extent that depends in part upon the nature of the system. The relationship between this correlation between input and output (crosscorrelation) and the systems impulse response forms the theoretical basis for the present method of measuring impulse response. If the random input is sufiiciently wideband so that it may be considered to be White noise, then the crosscorrelation becomes the equivalent of the impulse response of the system. Hence, the system impulse response can be determined by computing the crosscorrelation between the systems output and a suitably wide-band random input. The apparatus of FIG. 1 performs this operation. When the autocorrelation function of the test signal input is sufficiently narrow compared to the impulse response of the system being measured, the average value of the multiplier output Will correspond to the value of the impulse response at a particular time. In order to determine the impulse response at several different times, a plurality of different values of delay are used. The multiplier output also contains a random component which is filtered out in order to provide the desired average value. The systems output and hence the multipliers output will also contain responses to the command inputs and the external disturbances. As far as the measurement of impulse response is concerned, these contributions merely represent more noise which can be reduced or substantially eliminated by filtering.

It has been found that the mechanization of a crosscorrelator can be greatly simplified and the test results improved by utilizing a particular type of test signal rather than the pure random noise ordinarily contemplated for such apparatus. The test signal (not shown) is made binary in nature, having only two states of equal positive and negative amplitude about a zero reference. Also, the test signal is made a discrete-interval binary signal in which the transition times thereof are explicitly specified. This type of binary signal can be generated by sampling a very wide-band noise source every 1 seconds and setting the signal equal to plus 1 if the sample is positive and minus 1 if the sample is negative. If the minimum interval width is seconds, the autocorrelation function of the discrete-interval binary signal will be a triangular shaped pulse such as the pulse 27 of FIG. 2. For small values of 1 this autocorrelation function very closely approaches the ideal impulse input (a pulse of infinite magnitude and infinitely short duration with unit area).

An input noise sample of infinite duration or of a duration long relative to the other times in the system will also produce the single pulse autocorrelation function 27. Further simplifications in apparatus and improvements in performance are obtained by making the test signal of finite length and repeating it periodically. In particular. the size and complexity of the filters can be substantially reduced as the average value of the multipliers output is obtained in a much shorter time with the periodic signal. The autocorrelation function of a periodic function is also periodic with the same period. Thus the discrete-interval binary signal discussed above which produced the autocorrelation function 27, when made periodic with a period of Nr will have the autocorrelation function shown in FIG. 2. The periodicity will have no effect on the operation of the system if N1 is greater than the length of the significant part of the impulse response of the system. Another feature of the particular test signal of the present invention is the fact that its autocorrelation function is not asymptotic, but drops sharply to zero in contrast to the random interval noise input which has an autocorrelation function with marked asymptotes.

Thus it is seen that a crosscorrelator can be implemented with a signal source which provides a discreteinterval binary and periodic test signal which has a triangular autocorrelation function. With this test signal, the multiplier instrumentation is very simple since the system output need by multiplied either by plus 1 or minus 1. Also the filter instrumentation is greatly simplified because the required averaging time is greatly reduced.

The signal source 11 may constitute a memory in which the discrete-interval binary signal is stored and read out periodically to the systems input and the delay unit. It should be noted that not every signal will produce the desired autocorrelation function and it is necessary to check the autocorrelation function of the selected signal before using the same in the apparatus. The trial and error approach to preparing a suitable signal can be tedious and time-consuming and a method of synthesizing a signal which will have the desired autocorrelation function has been developed.

In particular, when N, the number of discrete intervals (bits) in one period, is a prime number, a test signal can be produced with the autocorrelation function shown in FIG. 3. When N is large (e.g., greater than it will be evident that this autocorrelation function will be substantially the same as that of FIG. 2. N is selected to be a prime number of the form 4K-1 where K=1, 2, 3, Then the binary state for each interval can be determined by either of the following expressions in which the sequentially solved valves for q represent the numbers of those intervals having a common binary state with the remaining intervals having the other binary state:

q =n for it less than N,

q :q -|-2n+l, for q less than N When q or q is greater than N, multiples of N may be substracted to provide a quantity less than N. The Nth interval can be either plus 1 or minus 1. In the autocorrelation function of FIG. 3, the last interval was minus 1. When the last interval is plus 1, the height of the horizontal portion of the curve will be plus 1 over N.

The following is a calculation of the numbers of the common intervals in the test signal for N=7 using the first formula q =m ,5 vq =.n for n less than 7. Hence (1 51 and g 4. When n2 s g a e a m t ples of 7 a substra ted from to Obtain a q nt y less tha 7- Thus s nee 3.= q3= =2- e s me resul a e obta n with the second formula (which is easier to mechanize) ,by obtaining the sequentially solved values for as follows:

Then the possible test signal sequences will have com.- mon binary terms for 1st, 2nd, and 4th intervals, and either binary term for the 7th interval, i.e.:

or the same sequences with all signs interchanged. Usually much larger values for N are used in actual systems.

It should be noted that the magnitude of this displacement from zero can be eliminated by making the last interval of the signal zero. However, this will make the test signal source ternary in nature, complicating the multiplication operation without producing any noticeable improvement in performance. Test signals with 251, 991 and 1019 intervals have been prepared using this approach. The ideal impulse is more closely approached by increasing the number of intervals per period and by shortening the duration of an interval. However, this increases the power requirements and complexity of the apparatus, and the selection of parameters for a particular embodiment is a comprise between performance and cost.

FlG. 4 shows a specific embodiment of the crosscorrelator which is particularly adapted for use with a periodic, discrete-interval binary test signal, and FIG. 5 shows the embodiment of FIG. 4 in greater detail. The apparatus of FIG. 4 includes a signal source 30, a shift register 31, a read-out circuit 32, a test signal storage unit 33, twelve delay signal storage units 34, twelve multiplier units 35, twelve filters 36, a display unit 37, and an inverter 38.

As shown in FIG. 5, the signal source 30 and shift register 31 can be implemented as separate tracks on a continuously rotating magnetic drum 42.

The test signal may be stored on one track 41 of drum 42. A second track 43 on the drum is used as a precessing circulating register to provide the desired time delay. A timing signal is stored on a third track 44 of the drum. The timing signal actuates a plurality of gates 45 in sequence to connect the shift registers output 46 to the test signal storage unit 33 and the delay signal storage units 34 in sequence. The timing signal and the plurality of gates function as a stepping switch or commutator which distributes the output from the shift register to the appropriate storage units. The shift register track 43, commutator 45, and storage units 34 correspond to the multichannel time delay 12 in the embodiment of FIG. 1 as well as register 31, commutator 32 and storage units 34 of FIG. 4.

The operation of each binary multiplier 35 is equivalent to that of a conventional single pole double throw relay 50, although ordinarily electronic switching circuits are utilized. Thinking of the multiplier as a relay, the output 19 of the system is supplied noninverted to one pole 51 of the relay and an inverted version of output 19 produced by an inverter 38 is supplied to the other pole 52. The moving arm 53 of the relay is connected to an associated filter 36. The relay is actuated by the delayed 6 signal t eat .the asses eted st r ge un t .t examp if the delayed signal is a plus 1, the output of the system will e diree ly sann eted to the fi ter a d a de a signal is a mirfus 1, the inver ed 9. will be connected to the filter. W

Similar eaer t ehs new: .in eaeh ef th twe ve hahne t eby rovid twe e a erag d output signals to the display unit. In the particularembodrment shown, the di play unit .is a a es e ray n eillnseep .5 wh h i upplied wi h the twe ve filter-humu via a s leeter switeh 56ISwitheh 56 yel ea ly eehh e s e eh filte output i sequence to th Ylaai a id simul aneously eenh etst t e X axis a deflee ieh eltase o value prop rtiona t e delay f th Particula sign l on the Y axis, th reby p in a po nt plo of the te aehse eharaeteris ie of t system along the X axis.

shoul h not d hat While t e emb dim n o FI 4 use twelve de ay d si nals, the eros eertel ter of the invention s not lim ted t parti u ar num r of .delasted sig als. In th s r a tieu hr app a us, th perio te t i nal had 991-inteivals with the' i hal be g rep once every 9.91 seconds. The shift register 991 bits in leng h an t e sh ft eom ahd oeehrred eve y hundredth of a second, hence requiring 9.91 seconds for the test signal to circulate through the register. The magnetic drum was driven at one hundred revolutions per second and the timing signal provided one commutation cycle per revolution. The natural frequencies of the system for which the crosscorrelator was built were expected to vary from two radians per second to twelve radians per second and an analysis of typical impulse responses in this range indicated that adequate test information could be obtained by utilizing twelve delay channels to provide twelve points on the impulse response curve with the delays ranging from 0.01 to 4.0 seconds. The majority of the points were concentrated in the lower time delay range.

In the actual instrument built as shown in FIG. 4, the delay unit was capable of providing delay of the order of ten or more seconds in increments of one hundredth of a second. This requires a shift register with the capacity to store of the order of one thousand bits of information. A conventional register of this size assembled from flipflops or magnetic cores is expensive and a magnetic drum circulating register as shown in FIG. 5 is more economical. However, where the maximum delay time is short or the information rate is relatively low, a shift register utilizing flip-flops may be substituted for the magnetic drum, with the delayed signals taken at appropriate outputs of the register.

Although exemplary embodiments of the present in vention have been disclosed and discussed, it will be understood that other applications of the invention are possible and that the embodiments disclosed may be subjected to various changes, modifications and substitutions without necessarily departing from the spirit of the invention.

We claim as our invention:

1. A test signal source for a crosseorrelator for measuring the impulse response of a system and including a signal delay unit, the combination of:

means for producing a periodic electrical pulse train having N discrete intervals, wherein N is a prime number of the form 4K-1, with K: 1, 2, 3, and where the sequentially solved values for where q define the intervals having one binary state with the remaining intervals having the other binary state and with the last interval having either stater, with q =n for n less than N, and for n greater than N, q =n -xN, where x=1, 2, 3, and

means for coupling said pulse train to the system as an input and to the delay unit as an input.

2. In a test signal source for a crosscorrelator for measuring the impulse response of a system and including a signal delay unit, the combination of:

a magnetic drum having first, second and third tracks,

with a discrete-inteval binary test signal stored on said first track and a timing signal stored on said 5. A test signal source for a crosscorrelator for measursecond track; ing the impulse response of a system and including a signal a precessing circulating register using said third track delay unit, the combination of:

with said test signal as an input; means for producing a discrete-interval binary and a first read circuit for said third track; periodic electrical pulse train; and a second read circuit for said second track; and means for coupling said pulse train to the system as an means for coupling said read circuit outputs to the input and to the delay unit as an input.

signal delay unit. 3. In a test signal source for a crosscorrelator for References Cited measuring the impulse response of a system and including m UNITED STATES PATENTS a signal delay unit, the combination of:

means for producing a discrete-interval binary electri- Anderson cal pulse train that is periodic with the period divided Westerfield' 2,177,347 4/1965 Cowley 235-181 X into a prime number of equal intervals, and 3 091 10/1965 means for coupling said pulse train to the system as an lssett et 235 181 X input and to the delay unit as an input. 4. In a test signal source for a crosscorrelator for OTHER REFERENCES measuring the impulse response of a system and including Anderson T self'Adiusting System For p a signal delay unit, the combination mum Dynamic Performance," IRE National Convention means for producing an electrical pulse train having an VOL P 4, March 1958; PP-

autocorrelation function havin the form of an isos- C6165 triangle; and g MALCOLM A. MORRISON, Primary Examiner. means for coupling said pulse train to the system as J. RUGGIERO, Assistant Examiner.

an input and to the delay unit as an input.

UNITED STATES PATENT OFFICE CERTIFICATE OF CORRECTION Patent No. 3,354,297 November 21, 1967 George W. Anderson et 211.

It is hereby certified that error appears in the above numbered patent requiring correction and that the said Letters Patent should read as corrected below.

Column 4, line 75, for "q =m read q =n column 6, line 11, for "Swithch" read Switch line 63, strike out "where".

Signed and sealed this 11th day of February 1969.

(SEAL) Attest:

Edward M. Fletcher, Jr. EDWARD J. BRENNER Attesting Officer Commissioner of Patents 

3. IN A TEST SIGNAL SOURCE FOR A CROSSCORRELATOR FOR MEASURING THE IMPULSE RESPONSE OF A SYSTEM AND INCLUDING A SIGNAL DELAY UNIT, THE COMBINATION OF: MEANS FOR PRODUCING A DISCRETE-INTERVAL BINARY ELECTRICAL PULSE TRAIN THAT IS PERIODIC WITH THE PERIOD DIVIDED INTO A PRIME NUMBER OF EQUAL INTERVALS; AND MEANS FOR COUPLING SAID PULSE TRAIN TO THE SYSTEM AS AN INPUT AND TO THE DELAY UNIT AS AN INPUT. 